Chaos and complexity in the dynamics of nonlinear Alfvén waves in a magnetoplasma

Subhrajit Roy; Animesh Roy; Amar P. Misra

doi:10.1063/5.0138866

journal article Feb 01, 2023

Chaos and complexity in the dynamics of nonlinear Alfvén waves in a magnetoplasma

Subhrajit Roy

Animesh Roy

Amar P. Misra

Chaos: An Interdisciplinary Journal of Nonlinear Science Vol. 33 No. 2 · AIP Publishing

View at Publisher Save 10.1063/5.0138866

Abstract

The nonlinear dynamics of circularly polarized dispersive Alfvén wave (AW) envelopes coupled to the driven ion-sound waves of plasma slow response is studied in a uniform magnetoplasma. By restricting the wave dynamics to a few number of harmonic modes, a low-dimensional dynamical model is proposed to describe the nonlinear wave–wave interactions. It is found that two subintervals of the wave number of modulation k of AW envelope exist, namely, (3/4)kc&lt;k&lt;kc and 0&lt;k&lt;(3/4)kc, where kc is the critical value of k below which the modulational instability (MI) occurs. In the former, where the MI growth rate is low, the periodic and/or quasi-periodic states are shown to occur, whereas the latter, where the MI growth is high, brings about the chaotic states. The existence of these states is established by the analyses of Lyapunov exponent spectra together with the bifurcation diagram and phase-space portraits of dynamical variables. Furthermore, the complexities of chaotic phase spaces in the nonlinear motion are measured by the estimations of the correlation dimension as well as the approximate entropy and compared with those for the known Hénon map and the Lorenz system in which a good qualitative agreement is noted. The chaotic motion, thus, predicted in a low-dimensional model can be a prerequisite for the onset of Alfvénic wave turbulence to be observed in a higher dimensional model that is relevant in the Earth’s ionosphere and magnetosphere.

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Details

Published: Feb 01, 2023
Vol/Issue: 33(2)

Authors

S

Subhrajit Roy

Department of Mathematics, Siksha Bhavana, Visva-Bharati University , Santiniketan 731 235, West Bengal, India

A

Animesh Roy

Department of Mathematics, Siksha Bhavana, Visva-Bharati University , Santiniketan 731 235, West Bengal, India

A

Amar P. Misra

Department of Mathematics, Siksha Bhavana, Visva-Bharati University , Santiniketan 731 235, West Bengal, India

Funding

Science and Engineering Research Board Award: CRG/2018/004475

Cite This Article

Subhrajit Roy, Animesh Roy, Amar P. Misra (2023). Chaos and complexity in the dynamics of nonlinear Alfvén waves in a magnetoplasma. Chaos: An Interdisciplinary Journal of Nonlinear Science, 33(2). https://doi.org/10.1063/5.0138866

Chaos and complexity in the dynamics of nonlinear Alfvén waves in a magnetoplasma

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